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Finding region of xy plane for which differential equation has... http://mathhelpboards.com/differential-equations-17/finding-r... Math Help Boards | Free Math Help Finding region of xy plane for which differential equation has a unique solution Printable View September 27th, 2013, 05:59 find_the_fun Finding region of xy plane for which differential equation has a unique solution Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0 , y0 ) in the region. x dy =y dx What does an xy-plane have to do with anything? I looked up the definition of unique solutions and here it is Let R be a rectangular region in the xy-planed defined by a <=x<=b, c<=y<=d that contains the point (x0 , y0 ) in its interior. If f(x,y) and ∂df ∂dy are continuous on R then there exists some interval I0 : (x0 − h, x0 + h), h > 0 contained in [a/b] and a unique function y(x) defined on I0 that is a solution of the initial value problem. That's a bit difficult to digest. How do I proceed? Fernando Revilla September 27th, 2013, 13:57 Re: Finding region of xy plane for which differential equation has a unique solution D ≡ x > 0 and D′ ≡ x < 0 the differential equation is equivalent to ∂f y 1 y′ = f (x, y) = , and in both regions, f and = are continuous, so and according to a well known x ∂y x theorem, D and D′ are solutions to your question. In each of the regions All times are GMT -4. The time now is 04:29. Powered by vBulletin Copyright © 2000 - 2012, Jelsoft Enterprises Ltd. © 2012-2014 Math Help Boards 1 de 1 18/02/14 09:30